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Thread: Please check my physics!

  1. #1

    Please check my physics!

    Let's say I'm super crazy. (A stretch, I know.)
    Let's say I mount two 500mm length steel rails 5mm from each other, and drive one positive and one negative.
    Let's say I have a way to feed 1/4" ball bearing steel balls onto these rails.
    Let's say it's all mounted in a slippery tube (oil nylon, or teflon) that keeps the ball on the rails if it bounces.

    How many amps of current do I need to deliver, for how long, to make the ball bearing exit the rails with a speed of 200 fps? (60 m/s)

    From what I can tell, I get 0.2 micronewtons times the square of the current (in amps,) and the ball weighs 1.05 grams.
    v = a * t = 60
    p = 0.5 = a * t * t / 2 = 60 * t / 2
    t = 1 / 60
    a = 1 = 2e-7 * c * c / 0.00105 = 0.000190 * c * c
    c = sqrt(1/0.000190) = 72.5 Amps


    That's ... not bad at all. What did I screw up in calculations? (The 0.2 micronewtons time amp squared seems the most suspect, as I couldn't get a really solid reference for that, just a mention that it's "definitionally" that way.)

    (Beacuse all robots need railguns.)

  2. #2
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    Re: Please check my physics!

    a = v/t
    d(t) = 0.5*a*t^2 + v0*t + d0
    E[J]= 0.5 * m[kg] * (v[m/s])^2 = 0.5 * c[F] * (x[V])^2

    0.5[m] = 0.5*a*t^2 = 0.5*(60/t)*t^2 => t = 1/60[s]
    a = 60[m/s] / (1/60)[s] = 3600[m/s^2]
    F = m*a = 0.00105[kg] * 3600[m/s^2] = 3.78[N]
    E = 0.5[J] * 0.00105[kg] * (60[m/s])^2 = 1.89[J]

    via ye pffft on railguns:
    F = ( (u0 * (I^2)) / (2*pi) ) * ln( (d-r)/r ); u0 = 4*pi*10^-7 [N/A^2]
    F[N] = ( (pi*4e-7)/(pi*2) )[N/A^2] * (I^2)[A^2] * ln( (d-r)/r ) = 2e-7[N/A^2] * (I^2)[A^2] * ln( (d-r)/r ); d=0.005[m]; r=?
    I[A] = sqrt( 3.78[N] / 2e-7[N/A^2] )

    or, alternatively, using assumption L' < 6e-7[H/m] == [N/A^2] as best case inductance of rails+armature per meter (likely significantly less, e.g. ~4e-7)
    F = ( (L')[N/A^2] * (I^2)[A^2] ) / 2
    I = sqrt( 3.78[N] / ((4e-7)/2)[N/A^2] ) = 4347[A]

    So, nope. Lots worse than 73[A] even with no frictional losses or resistive losses, although still only needed for ~0.017[s]. You need a capacitor bank with an energy capacity of at least 2[J] capable of dumping up to ~4500[A] for a fraction of a second without detonating.
    Please pardon the pedantry... and the profanity... and the convoluted speech pattern...
    "You have failed me, Brain!"
    [git][mech][hack]
    gives free advice only on public threads

  3. #3
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    Re: Please check my physics!

    A simple-ish alternative would be a coilgun using spring-loaded contacts in the bore to perform the commutation of the coils the using the projectile/armature/sabot. Each set of contacts would extend into the previous coil by quite a bit and end no later than the midpoint of the coil it commutates. If the contacts/rails are properly polarized, they would contribute a small force in addition to that of the coils/solenoids.
    Please pardon the pedantry... and the profanity... and the convoluted speech pattern...
    "You have failed me, Brain!"
    [git][mech][hack]
    gives free advice only on public threads

  4. #4

    Re: Please check my physics!

    In the rail gun case, the resistance isn't so much causing losses from the current I apply, as it prevents me from getting to the needed current level.

    1/8" * 3/8" rails have a resistance of 4.73 mOhm per meter -- and there's a meter of rails, so I only need 22 Volts. I'll want to drive the rails from the front, so as the voltage of the capacitors drops, the resistance drops, too.
    Unfortunately, ESR, and MOSFET Rdson, end up pushing that value up considerably. I also need to get something for the contact resistance between ball and rail.
    And ceramic caps (low ESR) are only available up to about 220 uF, and even so they're expensive arrays at that point. Like, many thousands of dollars to get there expensive.

    (The first Google hit for "steel resistance" is this, which I guess says something about our post-truth society?)

    So, assuming I had financial resources, the next challenge would be weight, and that's actually a challenge that not even money would solve.


    If I did a coil gun, I might as well sequence it using timing rather than switches? And perhaps some (optical?) positional sensor for timing the first bit of movement to synchronize the pulse?
    And I'd mainly have to divide out the needed current by the number of turns of the coils? (And the use enough voltage to compensate for the inductance.)
    Not as cool as the railgun thought, though :-)

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    Re: Please check my physics!

    Not too long after I first joined the forum, there was a discussion on railguns and/or coilguns that inspired a project that still has not really made it much beyond concept. I only finished a single small coil segment a few millimeters thick, but the idea was a coilgun with each segment resembling a bitter electromagnet/solenoid made from lengths of copper/aluminum foil repeatedly folded to form a square/octagonal coil with insulating film between each layer. The test wound up being a strip of cheap aluminum foil cut into a width 3~4" wide and laminated on one (or both?) side(s) with a layer of some paper, then folded to form a square coil ~6" on edge and square bore ~0.5" on edge. IIRC, each coil segment was to have exposed foil at each end of the segment for electrical connections then everything tightly clamped together with endplates and threaded rod, then potted with expoxy and additional plates on the outside of the potted coils to keep them from exploding during firing (like a coin shrinker coil).

    With a coilgun, you basically get the same strong magnetic field with far smaller currents than needed in a railgun because each loop increases the intensity of the field - sort of 'reusing' the current instead of just wasting it through just a single loop like the railgun. Increasing the number of loops also increases the inductance, which also increases resistance and slows its current response so the bitter electromagnet gets around that by using thin, wide plates of conductor sandwiched between insulators for very high currents and high loop counts per unit length of the coil.
    Please pardon the pedantry... and the profanity... and the convoluted speech pattern...
    "You have failed me, Brain!"
    [git][mech][hack]
    gives free advice only on public threads

  6. #6

    Re: Please check my physics!

    Running some simple numbers assuming 16 AWG transformer wire, the main problem is the very low resistance.
    A meter is 16 mOhms; ten turns around 10 mm diameter is about twelve inches covering just over a centimeter of the barrel; three layers makes for 1.2 meters which does mitigate the high currents.
    Add Rdson and ESR and you get another 0.015 milliohms or so. At 12V, 400A, three layers of 10 turns, it might be enough to accelerate the bearing.
    In fact, the field strength may be high enough that it saturates the carbon steel...

    I'd need about 0.13 Farads per coil; charge though 1-2 ohm resistors. Two of these per coil would do it:
    http://www.digikey.com/product-detai...2623-ND/757836
    Unfortunately, they're 35 mm large, so I'd need to stack them four out each side. Also, I'd get around 40 coils around the barrel, spaced in time over 16 milliseconds. I wonder if 12V is enough to drive the inductance of those coils, but I think it should be?
    Also, N-channels, and gate drivers and stuff. Not really hard.
    http://www.digikey.com/product-detai...5-1-ND/2697057

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    Re: Please check my physics!

    In 2012 at Robogames a fellow from, I think, Brazil entered Mechwarfare. He traveled with two Mechs. One of them he competed with using Fatshark glasses at 5.8Ghz. Maybe someone else might remember him. He ended up being disqualified near the end by Andrew because his mech kept firing off out of control where people were. Also I think he was firing rockets in the pit area. Anyway, his second mech had a railgun. He did not compete with it because the body was made out of carbon fiber and on the way from Brazil he shorted his high voltage power supply thru a gas discharge tube into his carbon body and bricked his entire mech. I remember checking out the mech in the pits. Before everything broke he claimed the rail gun worked fine. I probably have remembered this a little wrong but the take away is he claimed he had a working rail gun.

  8. #8

    Re: Please check my physics!

    he shorted his high voltage power supply thru a gas discharge tube into his carbon body and bricked his entire mech
    That's amazing and sad at the same time!

  9. #9
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    Re: Please check my physics!

    As long as you have enough in parallel, cheap electrolytic capacitors would likely work well enough to provide the bulk of the capacitance. Just keep a small portion of the array as some lower ESR/impedance capacitors (ceramic or thin film) for the rapid current change and add some reverse voltage protection for the polarized electrolytic caps.

    Have five 3uF thin film and one 82uF electrolytic rated at 400V that I got several years ago as part of a mystery box from electronics goldmine. Thinking they were going to be part of the foil coil gun, or maybe a tesla coil. The single larger thin film cap from that mystery box is about the size of a 90-day pill bottle from CVS and rated 40uF, but only up to 250V. Hmm... thinking there is still a bag of steel slingshot BBs somewhere and 200V would permit using all 137uF of the high-ish voltage capacitors while still getting ~2.74J of energy storage. Would probably just reuse some of the cheap 6063 aluminum angle salvaged from Darsha's first chassis and screwed down onto some scrap wood board for test rails. Safely charging up to 200V would be the only slightly difficult part, but split-phase 110V would be easy enough to start with since I've got several bridge rectifiers not doing anything.
    Please pardon the pedantry... and the profanity... and the convoluted speech pattern...
    "You have failed me, Brain!"
    [git][mech][hack]
    gives free advice only on public threads

  10. #10

    Re: Please check my physics!

    cheap electrolytic capacitors would likely work well enough to provide the bulk of the capacitance
    Electrolytic caps with 10 mOhm ESR aren't that expensive. A couple of those in parallel and you're looking at 5 mOhm effective.
    Higher voltage might be better because of the lower loss in the lower amperage, and perhaps make up the difference in number of turns?

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